Aparate de sloturi cu 3 role
2. Cazul B – numere diferite de stopuri si distributii
diferite de simboluri pe role
2.8
Un anumit simbol cel putin de doua ori
Probabilitatea acestui eveniment este
,
unde 
sunt
probabilitatile de baza ale aparitiei acelui simbol pe role respectiv. In
cazul particular in care doua din cele trei role au acelasi numar de stopuri si
aceleasi distributii de simboluri, probabilitatea evenimentului masurat este
,
undee 
este
probabilitatea de baza a aparitiei acelui simbol pe una din cele doua role
similare, iar 
este
probabilitatea de baza a aparitiei acelui simbol pe ce-a de-a treia rola.
Aceasta formula particulara genereaza urmatoarele tabele de valori, unde
valorile probabilitatilor de baza sunt listate cu increment de 0.005, de la 0.005
la
0.100, iar fiecare tabel listeaza sapte valori ale lui
.
Tabele de valori ale probabilitatii de aparitie a unui anumit simbol de cel
putin doua ori pe o linie de castig
Tabel 1:
de
la 0.005 la 0.035
|
|
0.005 |
0.010 |
0.015 |
0.020 |
0.025 |
0.030 |
0.035 |
|
|
|
0.005 |
0.00007475 |
0.0001245 |
0.00017425 |
0.000224 |
0.00027375 |
0.0003235 |
0.00037325 |
|
0.01 |
0.000199 |
0.000298 |
0.000397 |
0.000496 |
0.000595 |
0.000694 |
0.000793 |
|
0.015 |
0.00037275 |
0.0005205 |
0.00066825 |
0.000816 |
0.00096375 |
0.0011115 |
0.00125925 |
|
0.02 |
0.000596 |
0.000792 |
0.000988 |
0.001184 |
0.00138 |
0.001576 |
0.001772 |
|
0.025 |
0.00086875 |
0.0011125 |
0.00135625 |
0.0016 |
0.00184375 |
0.0020875 |
0.00233125 |
|
0.03 |
0.001191 |
0.001482 |
0.001773 |
0.002064 |
0.002355 |
0.002646 |
0.002937 |
|
0.035 |
0.00156275 |
0.0019005 |
0.00223825 |
0.002576 |
0.00291375 |
0.0032515 |
0.00358925 |
|
0.04 |
0.001984 |
0.002368 |
0.002752 |
0.003136 |
0.00352 |
0.003904 |
0.004288 |
|
0.045 |
0.00245475 |
0.0028845 |
0.00331425 |
0.003744 |
0.00417375 |
0.0046035 |
0.00503325 |
|
0.05 |
0.002975 |
0.00345 |
0.003925 |
0.0044 |
0.004875 |
0.00535 |
0.005825 |
|
0.055 |
0.00354475 |
0.0040645 |
0.00458425 |
0.005104 |
0.00562375 |
0.0061435 |
0.00666325 |
|
0.06 |
0.004164 |
0.004728 |
0.005292 |
0.005856 |
0.00642 |
0.006984 |
0.007548 |
|
0.065 |
0.00483275 |
0.0054405 |
0.00604825 |
0.006656 |
0.00726375 |
0.0078715 |
0.00847925 |
|
0.07 |
0.005551 |
0.006202 |
0.006853 |
0.007504 |
0.008155 |
0.008806 |
0.009457 |
|
0.075 |
0.00631875 |
0.0070125 |
0.00770625 |
0.0084 |
0.00909375 |
0.0097875 |
0.01048125 |
|
0.08 |
0.007136 |
0.007872 |
0.008608 |
0.009344 |
0.01008 |
0.010816 |
0.011552 |
|
0.085 |
0.00800275 |
0.0087805 |
0.00955825 |
0.010336 |
0.01111375 |
0.0118915 |
0.01266925 |
|
0.09 |
0.008919 |
0.009738 |
0.010557 |
0.011376 |
0.012195 |
0.013014 |
0.013833 |
|
0.095 |
0.00988475 |
0.0107445 |
0.01160425 |
0.012464 |
0.01332375 |
0.0141835 |
0.01504325 |
|
0.1 |
0.0109 |
0.0118 |
0.0127 |
0.0136 |
0.0145 |
0.0154 |
0.0163 |
Tabel 2:
de
la
0.040 la 0.070
|
|
0.040 |
0.045 |
0.050 |
0.055 |
0.060 |
0.065 |
0.070 |
|
|
|
0.005 |
0.000423 |
0.00047275 |
0.0005225 |
0.00057225 |
0.000622 |
0.00067175 |
0.0007215 |
|
0.01 |
0.000892 |
0.000991 |
0.00109 |
0.001189 |
0.001288 |
0.001387 |
0.001486 |
|
0.015 |
0.001407 |
0.00155475 |
0.0017025 |
0.00185025 |
0.001998 |
0.00214575 |
0.0022935 |
|
0.02 |
0.001968 |
0.002164 |
0.00236 |
0.002556 |
0.002752 |
0.002948 |
0.003144 |
|
0.025 |
0.002575 |
0.00281875 |
0.0030625 |
0.00330625 |
0.00355 |
0.00379375 |
0.0040375 |
|
0.03 |
0.003228 |
0.003519 |
0.00381 |
0.004101 |
0.004392 |
0.004683 |
0.004974 |
|
0.035 |
0.003927 |
0.00426475 |
0.0046025 |
0.00494025 |
0.005278 |
0.00561575 |
0.0059535 |
|
0.04 |
0.004672 |
0.005056 |
0.00544 |
0.005824 |
0.006208 |
0.006592 |
0.006976 |
|
0.045 |
0.005463 |
0.00589275 |
0.0063225 |
0.00675225 |
0.007182 |
0.00761175 |
0.0080415 |
|
0.05 |
0.0063 |
0.006775 |
0.00725 |
0.007725 |
0.0082 |
0.008675 |
0.00915 |
|
0.055 |
0.007183 |
0.00770275 |
0.0082225 |
0.00874225 |
0.009262 |
0.00978175 |
0.0103015 |
|
0.06 |
0.008112 |
0.008676 |
0.00924 |
0.009804 |
0.010368 |
0.010932 |
0.011496 |
|
0.065 |
0.009087 |
0.00969475 |
0.0103025 |
0.01091025 |
0.011518 |
0.01212575 |
0.0127335 |
|
0.07 |
0.010108 |
0.010759 |
0.01141 |
0.012061 |
0.012712 |
0.013363 |
0.014014 |
|
0.075 |
0.011175 |
0.01186875 |
0.0125625 |
0.01325625 |
0.01395 |
0.01464375 |
0.0153375 |
|
0.08 |
0.012288 |
0.013024 |
0.01376 |
0.014496 |
0.015232 |
0.015968 |
0.016704 |
|
0.085 |
0.013447 |
0.01422475 |
0.0150025 |
0.01578025 |
0.016558 |
0.01733575 |
0.0181135 |
|
0.09 |
0.014652 |
0.015471 |
0.01629 |
0.017109 |
0.017928 |
0.018747 |
0.019566 |
|
0.095 |
0.015903 |
0.01676275 |
0.0176225 |
0.01848225 |
0.019342 |
0.02020175 |
0.0210615 |
|
0.1 |
0.0172 |
0.0181 |
0.019 |
0.0199 |
0.0208 |
0.0217 |
0.0226 |
Tabel 3:
de
la
0.075 la 0.105
|
|
0.075 |
0.080 |
0.085 |
0.090 |
0.095 |
0.100 |
0.105 |
|
|
|
0.005 |
0.00077125 |
0.000821 |
0.00087075 |
0.0009205 |
0.00097025 |
0.00102 |
0.00106975 |
|
0.01 |
0.001585 |
0.001684 |
0.001783 |
0.001882 |
0.001981 |
0.00208 |
0.002179 |
|
0.015 |
0.00244125 |
0.002589 |
0.00273675 |
0.0028845 |
0.00303225 |
0.00318 |
0.00332775 |
|
0.02 |
0.00334 |
0.003536 |
0.003732 |
0.003928 |
0.004124 |
0.00432 |
0.004516 |
|
0.025 |
0.00428125 |
0.004525 |
0.00476875 |
0.0050125 |
0.00525625 |
0.0055 |
0.00574375 |
|
0.03 |
0.005265 |
0.005556 |
0.005847 |
0.006138 |
0.006429 |
0.00672 |
0.007011 |
|
0.035 |
0.00629125 |
0.006629 |
0.00696675 |
0.0073045 |
0.00764225 |
0.00798 |
0.00831775 |
|
0.04 |
0.00736 |
0.007744 |
0.008128 |
0.008512 |
0.008896 |
0.00928 |
0.009664 |
|
0.045 |
0.00847125 |
0.008901 |
0.00933075 |
0.0097605 |
0.01019025 |
0.01062 |
0.01104975 |
|
0.05 |
0.009625 |
0.0101 |
0.010575 |
0.01105 |
0.011525 |
0.012 |
0.012475 |
|
0.055 |
0.01082125 |
0.011341 |
0.01186075 |
0.0123805 |
0.01290025 |
0.01342 |
0.01393975 |
|
0.06 |
0.01206 |
0.012624 |
0.013188 |
0.013752 |
0.014316 |
0.01488 |
0.015444 |
|
0.065 |
0.01334125 |
0.013949 |
0.01455675 |
0.0151645 |
0.01577225 |
0.01638 |
0.01698775 |
|
0.07 |
0.014665 |
0.015316 |
0.015967 |
0.016618 |
0.017269 |
0.01792 |
0.018571 |
|
0.075 |
0.01603125 |
0.016725 |
0.01741875 |
0.0181125 |
0.01880625 |
0.0195 |
0.02019375 |
|
0.08 |
0.01744 |
0.018176 |
0.018912 |
0.019648 |
0.020384 |
0.02112 |
0.021856 |
|
0.085 |
0.01889125 |
0.019669 |
0.02044675 |
0.0212245 |
0.02200225 |
0.02278 |
0.02355775 |
|
0.09 |
0.020385 |
0.021204 |
0.022023 |
0.022842 |
0.023661 |
0.02448 |
0.025299 |
|
0.095 |
0.02192125 |
0.022781 |
0.02364075 |
0.0245005 |
0.02536025 |
0.02622 |
0.02707975 |
|
0.1 |
0.0235 |
0.0244 |
0.0253 |
0.0262 |
0.0271 |
0.028 |
0.0289 |
Exemplu
de utilizare a tabelelor:
Gasiti probabilitatea de aparitie a cel putin doua cirese pe o linie de castig a
unui aparat de sloturi cu 3 role, avand 65, 65, 68 stopuri pe rolele 1, 2, 3 respectiv
si 2, 2, 1 cirese pe aceste role respectiv.
Suntem in cazul particular a doua role similare (1 si 2). 
si
.
Urmarim Tabelul 1 si cautam la intersectia coloanei
cu
linia 
,
unde gasim probabilitatea 0.002646. Putem lua 0.0025 = 0.25% ca o aproximare a
probabilitatii cautate. Pentru un rezultat exact, trebuie aplicata direct
formula care a generat tabelele.